함수 전체 문제

If $a$ varies directly as $b$ and $a=6,\,\text{when}\,b=\frac{1}{3}$, find the equation that relates $a\,\text{and}\,b.$

If $v$ varies directly as $w$ and $v=8,\,\text{when}\,w=\frac{1}{2}$, find the equation that relates $v\,\text{and}\,w.$

The amount of money Sally earns, P, varies directly with the number, n, of necklaces she sells. When Sally sells 15 necklaces she earns $150.

• ⓐ Write the equation that relates P and n.
• ⓑ How much money would she earn if she sold 4 necklaces?

Terri needs to make some pies for a fundraiser. The number of apples, a, varies directly with number of pies, p. It takes nine apples to make two pies.

• ⓐ Write the equation that relates a and p.
• ⓑ How many apples would Terri need for six pies?

The length that a spring stretches varies directly with a weight placed at the end of the spring. When Sarah placed a 10 pound watermelon on a hanging scale, the spring stretched 5 inches.

• ⓐ Write the equation that relates the length of the spring to the weight.
• ⓑ What weight of watermelon would stretch the spring 6 inches?

The maximum load a beam will support varies directly with the square of the diagonal of the beam’s cross-section. A beam with diagonal 6 inch will support a maximum load of 108 pounds.

• ⓐ Write the equation that relates the load to the diagonal of the cross-section.
• ⓑ What load will a beam with a 10 inch diagonal support?

If $y$ varies inversely with $x$ and $y=5$ when $x=4$ find the equation that relates $x$ and $y.$

If $p$ varies inversely with $q$ and $p=2$ when $q=1$ find the equation that relates $p$ and $q.$

If $v$ varies inversely with $w$ and $v=6$ when $w=\frac{1}{2}$ find the equation that relates $v$ and $w.$

If $a$ varies inversely with $b$ and $a=12$ when $b=\frac{1}{3}$ find the equation that relates $a$ and $b.$

The fuel consumption (mpg) of a car varies inversely with its weight. A Toyota Corolla weighs 2800 pounds and gets 33 mpg on the highway.

• ⓐ Write the equation that relates the mpg to the car’s weight.
• ⓑ What would the fuel consumption be for a Toyota Sequoia that weighs 5500 pounds?

A car’s value varies inversely with its age. Jackie bought a 10 year old car for $2,400.

• ⓐ Write the equation that relates the car’s value to its age.
• ⓑ What will be the value of Jackie’s car when it is 15 years old ?

The number of tickets for a sports fundraiser varies inversely to the price of each ticket. Brianna can buy 25 tickets at $5each.

• ⓐ Write the equation that relates the number of tickets to the price of each ticket.
• ⓑ How many tickets could Brianna buy if the price of each ticket was $2.50?

If $y$ varies directly as $x$ and $y=5,\,\text{when}\,x=3.$, find the equation that relates $x\,\text{and}\,y$.

If $v$ varies directly as $w$ and $v=21,\,\text{when}\,w=8.$ find the equation that relates $v\,\text{and}\,w.$

If $p$ varies inversely with $q$ and $p=5$ when $q=6$, find the equation that relates $p$ and $q.$

If $y$ varies inversely with $x$ and $y=11$ when $x=3$ find the equation that relates $x$ and $y.$

If $p$ varies directly as $q$ and $p=10,\,\text{when}\,q=2.$ find the equation that relates $p\,\text{and}\,q$.

If $v$ varies inversely with $w$ and $v=18$ when $w=\frac{1}{3}$ find the equation that relates $v$ and $w.$

The force needed to break a board varies inversely with its length. If Tom uses 20 pounds of pressure to break a 1.5-foot long board, how many pounds of pressure would he need to use to break a 6 foot long board?